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Anomalous Majorana Neutrino Masses from Torsionful Quantum Gravity

The effect of quantum torsion in theories of quantum gravity is usually described by an axion-like field which couples to matter and to gravitation and radiation gauge fields. In perturbation theory, the couplings of this torsion-descent axion field are of derivative type and so preserve a shift symmetry. This shift symmetry may be broken, if the torsion-descent axion field mixes with other axions, which could be related to moduli fields in string-inspired effective theories. In particular, the shift symmetry may break explicitly via non-perturbative effects, when these axions couple to fermions via chirality changing Yukawa couplings with appropriately suppressed coefficients. We show, how in such theories an effective right-handed Majorana neutrino mass can be generated at two loops by gravitational interactions that involve global anomalies related to quantum torsion. We estimate the magnitude of the gravitationally induced Majorana mass and find that it is highly model dependent, ranging from multi-TeV to keV scale.